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Proof of inverse derivative

Petrus

Well-known member
Feb 21, 2013
739
Hello MHB,
I am aware of there is two way, u can use chain rule or defination of derivate. I totaly understand the proof with this type Derivative of Inverse Function but is that a valid proof? How ever our teacher did proof this with derivate defination which I dont understand from my textbook. What is your thought? Any good link that explain this proof with derivate defination

I am aware that we use chain rule and im training for oral exam and I guess I will have to proof this chain rule in this one.

edit: why should \(\displaystyle f'(x) \neq 0\) should it be \(\displaystyle f'(y) \neq 0\)
Regards,
\(\displaystyle |\pi\rangle\)
 
Last edited:

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,774
re: proof of inverse derivative

Hello MHB,
I am aware of there is two way, u can use chain rule or defination of derivate. I totaly understand the proof with this type Derivative of Inverse Function but is that a valid proof? How ever our teacher did proof this with derivate defination which I dont understand from my textbook. What is your thought? Any good link that explain this proof with derivate defination

I am aware that we use chain rule and im training for oral exam and I guess I will have to proof this chain rule in this one.

edit: why should \(\displaystyle f'(x) \neq 0\) should it be \(\displaystyle f'(y) \neq 0\)
Regards,
\(\displaystyle |\pi\rangle\)
That proof looks valid to me.

Note that there may be some confusion about x and y, since their meanings are swapped around after the first line.
In the first line x is used as the argument of f, but in the second line and thereafter x is used as the argument of $f^{-1}$ instead (where you might expect y to be the argument).
 

Petrus

Well-known member
Feb 21, 2013
739
Re: proof of inverse derivative

That proof looks valid to me.

Note that there may be some confusion about x and y, since their meanings are swapped around after the first line.
In the first line x is used as the argument of f, but in the second line and thereafter x is used as the argument of $f^{-1}$ instead (where you might expect y to be the argument).
Thanks for taking your time I like Serena!:)

PS. Should I be rational or real:p

Regards,
\(\displaystyle |\pi\rangle\)
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,774
Re: proof of inverse derivative

Thanks for taking your time I like Serena!:)

PS. Should I be rational or real:p

Regards,
\(\displaystyle |\pi\rangle\)
I think that \(\displaystyle |\pi\rangle\) is imaginary. (Pizza)